Our research group at Indiana University is investigating a formalization of digital system design that is based on functional algebra. We have developed a transformation system called DDD to facilitate this study. DDD stands for digital design derivation; the system is used interactively to translate higher level specifications into hierarchical boolean systems, to which logic synthesis tools are then applied. In this paper, we take a detailed look at how the system is used. In two examples, we examine the sequence of intermediate expressions produced as an implementation is derived. We discuss how these expressions are used at strategic levels of thinking. We illustrate how the choice of target technology influences the tactical course of derivation. Throughout, we try to give a sense of how functional abstractions are manipulated in the engineering process.